Question

What is NOT a real number?

Answer 1

Hint: The definition of a real number is the combinational of rational and irrational numbers. We will also explore the terms rational numbers, irrational numbers and imaginary numbers by writing their definitions and general forms. And so, we will deduce such a definition to deduce a non-real number.

Complete step-by-step solution:
We have been asked in this question as to what is not a real number. As we know real numbers are a combination of rational and irrational numbers. So, let us first look at the definitions of both of them. A rational number is that which can be deduced in the form of $\dfrac{p}{q}$, where p and q are integers and $q\ne 0$. Whereas an irrational number is a non-terminating and non-repeating number. Since we know that the non-terminating and the non-repeating terms can be converted to the $\dfrac{p}{q}$ from, we can say that there is another category of numbers that fall into the category of non-real numbers. They are called imaginary numbers. The imaginary numbers are symbolised as ‘i’ and they are also called iota. It is generally depicted as, $i=\sqrt{-1}$. Since this is generally not defined and hence is given a special place in the number system.

Note: We should remember that any square root of a negative number is an imaginary number. For example, if we take, $\sqrt{-2}$, then it’s square root will be, $\sqrt{-2}=\sqrt{2}\times \sqrt{-1}=\sqrt{2}i$. So, overall $\sqrt{-2}$ is an imaginary number.